electrostatic induction
Electrostatic induction is the way a charged object can rearrange the charges in a nearby object without ever touching it. Hold a charged balloon near a thin stream of tap water and the stream bends toward it; hold it near small paper bits and they leap up to it. The balloon never touches them, yet it pulls, because it has induced charge to shift inside them.
Here is how it works in a conductor. Bring a positive rod near a neutral metal sphere: the sphere's free electrons are attracted and pile up on the near side, leaving the far side positive. The sphere is still neutral overall, but now its near side is negative, and since that negative side is closer to the rod, the attraction beats the repulsion of the far side, so the sphere is pulled in. In an insulator the charges cannot travel, but each molecule stretches slightly (it polarizes), giving the same net attraction more weakly.
Induction also lets you charge an object without contact, called charging by induction: bring a charged rod close, briefly ground the far side so some charge escapes, then remove the ground and the rod, and the object is left with a net charge of the opposite sign. This is why a charged comb picks up neutral scraps of paper, and it is the basis of touchscreens and many sensors.
Rub a plastic comb on your sleeve and hold it above tiny paper bits; the comb induces opposite charge on the near face of each bit, and they jump up and stick, though they started neutral.
A charged object attracts a neutral one by inducing opposite charge on its near side.
Induction rearranges charge; it does not require any charge to jump across. A charged object attracts a neutral one precisely because the near side's induced charge is closer than the far side's.